Going Around in Circles! Advanced Geometry 10.1 and 10.2

Parts of a Circle and their Definitions Circle –Set of all points in a plane that are a given distance from a given point in the plane. Given point Given distance CENTER RADIUS Center The given point referred to in the definition of the circle. A circle is named by its center! Radius The given distance referred to in the circle definition – the segment connecting the center to the circle – the distance from the center to the circle.

Parts of a Circle and their Definitions Concentric Circles Two or more coplanar circles with the same center

Parts of a Circle and their Definitions A point is inside (in the interior) a circle if its distance from the center is less than the radius. INTERIOR of a circle EXTERIOR of a circle A point is outside (in the exterior) a circle if its distance from the center is more than the radius. POINT on a circle A point is on a circle if the distance from the center is equal to the radius.

Parts of a Circle and their Definitions Chord A chord of a circle is a segment that connects any two points on the circle. A chord that passes through the center is called the DIAMETER of the circle

Parts of a Circle and their Definitions Circumference The perimeter of or distance around a circle is called the circumference of a circle. C = 2πr or πd Check out about how the circumference of the earth was foundcircumference of the earth

Parts of a Circle and their Definitions Area of a Circle

Theorems for Circle Radii and Chords If a radius is perpendicular to a chord then it bisects the chord If a radius of a circle bisects a chord that is not a diameter, then it is perpendicular to that chord. The perpendicular bisector of a chord passes through the center of the circle.

Example 1 (10.1)..... P Q S T R

Example 1 (10.1).

Example 3 (10.1) A BC s.. QP

Example 3 (10.1) s

Theorems for Circle Congruent Chords If two chords of a circle are equidistant from the center, then they are congruent. If two chords of a circle are congruent, then they are equidistant from the center of the circle.

Example 1 (10.2). B C P Q O AD

Example 2 (10.2). A B R C P Q

Example 2 (10.2)

HOMEWORK!!!!!!!!!!!! Pg , 9, 10, 15 Pg , 8, 9,11, 12 Index Cards for 10.3

Exit Slip 1. If two chords of a circle are ____ from the center, then they are ____. 2. State the formula for the area of a circle. 3. A ____ of a circle is a segment joining any two points on the circle.